# Help with conceptualising a problem.

I've been considering shapes formed when we take $$n$$-tuple such as $$\{0,1,2\}$$ and plot all permutations forming a shape (for $$n=2$$ its a line, for $$n=3$$ it's a hexagon). However I'm having trouble trying to understand the plot for $$n=4$$, mainly because it's in 4D and that's hard to plot. I feel as though it's just going to make $$n!$$-polygon. I'm in high school so I don't really have a rigorous mathematical training hence why I'm looking for some guidance in how to approach such problems.

• It seems to me that you are rediscovering this construction: en.wikipedia.org/wiki/Permutohedron Cool :-) – Lorenzo Mar 28 at 21:49
• Oh thanks I was just thinking about ways of making the superpermutations problem geometric so it's nice that people have thought of this before. – John Miller Mar 28 at 21:50